YES

Problem:
 p(0()) -> 0()
 p(s(x)) -> x
 minus(x,0()) -> x
 minus(x,s(y)) -> minus(p(x),y)

Proof:
 DP Processor:
  DPs:
   minus#(x,s(y)) -> p#(x)
   minus#(x,s(y)) -> minus#(p(x),y)
  TRS:
   p(0()) -> 0()
   p(s(x)) -> x
   minus(x,0()) -> x
   minus(x,s(y)) -> minus(p(x),y)
  Usable Rule Processor:
   DPs:
    minus#(x,s(y)) -> p#(x)
    minus#(x,s(y)) -> minus#(p(x),y)
   TRS:
    p(0()) -> 0()
    p(s(x)) -> x
   CDG Processor:
    DPs:
     minus#(x,s(y)) -> p#(x)
     minus#(x,s(y)) -> minus#(p(x),y)
    TRS:
     p(0()) -> 0()
     p(s(x)) -> x
    graph:
     minus#(x,s(y)) -> minus#(p(x),y) -> minus#(x,s(y)) -> p#(x)
     minus#(x,s(y)) -> minus#(p(x),y) -> minus#(x,s(y)) -> minus#(p(x),y)
    Restore Modifier:
     DPs:
      minus#(x,s(y)) -> p#(x)
      minus#(x,s(y)) -> minus#(p(x),y)
     TRS:
      p(0()) -> 0()
      p(s(x)) -> x
      minus(x,0()) -> x
      minus(x,s(y)) -> minus(p(x),y)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 2/4
      DPs:
       minus#(x,s(y)) -> minus#(p(x),y)
      TRS:
       p(0()) -> 0()
       p(s(x)) -> x
       minus(x,0()) -> x
       minus(x,s(y)) -> minus(p(x),y)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [minus#](x0, x1) = x1,
        
        [minus](x0, x1) = x0,
        
        [s](x0) = x0 + 1,
        
        [p](x0) = x0,
        
        [0] = 0
       orientation:
        minus#(x,s(y)) = y + 1 >= y = minus#(p(x),y)
        
        p(0()) = 0 >= 0 = 0()
        
        p(s(x)) = x + 1 >= x = x
        
        minus(x,0()) = x >= x = x
        
        minus(x,s(y)) = x >= x = minus(p(x),y)
       problem:
        DPs:
         
        TRS:
         p(0()) -> 0()
         p(s(x)) -> x
         minus(x,0()) -> x
         minus(x,s(y)) -> minus(p(x),y)
       Qed